The broad goals of this project are to develop and analyze mathematical models of the dynamics of demographic change, and to apply these models to understand significant questions in historical and economic demography. One class of models to be investigated extends the classical demographic models to take account of exogenous and endogeneous forces which have dynamical consequences; in particular the steady-state and transient properties of stochastic density-independent and stochastic density-dependent models will be analyzed. A second class of models will consider two-sexes and parity-progression. A third class of models will embed the demographic dynamics in the context of economically and politically driven secular change. In each case the focus will be on specific models for human populations with the analysis to be carried through to the point where significant qualitative and quantitative demographic questions can be answered. Some specific questions to be examined are: the projection of averages and confidence intervals for steady-state, and transient stochastic demographic models; the estimation of density-dependent forces using fertility data and the impact of density on dynamics for populations far from and near stationary growth; the dynamics of population structure under the impact of secular changes in fertility and mortality which are characteristic of developed countries and LDCs; the robustness of estimation techniques in nonequilibrium populations; the linkage between migration rates, growth rates and fertility in LDC's; sequential decision-making, target fertility and the causes of inequality.